Frequency Estimation of Correlated Multi-attribute Data under Local Differential Privacy

Abstract: Large-scale data collection, from national censuses to IoT-enabled smart homes, routinely gathers dozens of attributes per individual. These multi-attribute datasets are vital for analytics but pose significant privacy risks. Local Differential Privacy (LDP) is a powerful tool to protect user data privacy by allowing users to locally perturb their records before releasing to an untrusted data aggregator. However, existing LDP mechanisms either split the privacy budget across all attributes or treat each attribute independently, ignoring natural inter-attribute correlations. This leads to excessive noise or fragmented budgets, resulting in significant utility loss, particularly in high-dimensional settings. To overcome these limitations, we propose Correlated Randomized Response (Corr-RR), a novel LDP mechanism that leverages correlations among attributes to substantially improve utility while maintaining rigorous LDP guarantees. Corr-RR allocates the full privacy budget to perturb a single, randomly selected attribute and reconstructs the remaining attributes using estimated interattribute dependencies, without incurring additional privacy cost. To enable this, Corr-RR operates in two phases: (1) a subset of users apply standard LDP mechanisms to estimate correlations, and (2) each remaining user perturbs one attribute and infers the others using the learned correlations. We theoretically prove that Corr-RR satisfies $\epsilon$-LDP, and extensive experiments on synthetic and real-world datasets demonstrate that Corr-RR consistently outperforms state-of-the-art LDP mechanisms, particularly in scenarios with many attributes and strong inter-attribute correlations.